Contents

# ?ggbal

Balances a pair of general real or complex matrices.

## Syntax

Include Files
• mkl.h
Description
The routine balances a pair of general real/complex matrices (
A
,
B
). This involves, first, permuting
A
and
B
by similarity transformations to isolate eigenvalues in the first 1 to
ilo
-1 and last
ihi
+1 to
n
elements on the diagonal;and second, applying a diagonal similarity transformation to rows and columns
ilo
to
ihi
to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem
A
*
x
=
λ
*
B
*
x
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
job
Specifies the operations to be performed on
A
and
B
. Must be
'N'
or
'P'
or
'S'
or
'B'
.
If
job
=
'N '
, then no operations are done; simply set
ilo
=1
,
ihi
=
n
,
lscale
[
i
]
=1.0
and
rscale
[
i
]
=1.0
for
i
= 0,...,
n
- 1
.
If
job
=
'P'
, then permute only.
If
job
=
'S'
, then scale only.
If
job
=
'B'
, then both permute and scale.
n
The order of the matrices
A
and
B
(
n
0).
a
,
b
Arrays:
a
(size max(1,
lda
*
n
))
contains the matrix
A
.
b
(size max(1,
ldb
*
n
))
contains the matrix
B
.
If
job
=
'N'
,
a
and
b
are not referenced.
lda
The leading dimension of
a
; at least max(1,
n
).
ldb
The leading dimension of
b
; at least max(1,
n
).
Output Parameters
a
,
b
Overwritten by the balanced matrices
A
and
B
, respectively.
ilo
,
ihi
ilo
and
ihi
are set to integers such that on exit
A
i
,
j
= 0 and
B
i
,
j
= 0 if
i
>
j
and
j
=1,...,
ilo
-1
or
i
=
ihi
+1,...,
n
.
If
job
=
'N'
or
'S'
, then
ilo
= 1
and
ihi
=
n
.
lscale
,
rscale
Arrays, size at least max(1,
n
).
lscale
contains details of the permutations and scaling factors applied to the left side of
A
and
B
.
If
P
j
is the index of the row interchanged with row
j
, and
D
j
is the scaling factor applied to row
j
, then
lscale
[
j
- 1]
=
P
j
, for
j
= 1,...,
ilo
-1
=
D
j
, for
j
=
ilo
,...,
ihi
=
P
j
, for
j
=
ihi
+1,...,
n
.
rscale
contains details of the permutations and scaling factors applied to the right side of
A
and
B
.
If
P
j
is the index of the column interchanged with column
j
, and
D
j
is the scaling factor applied to column
j
, then
rscale
[
j
- 1]
=
P
j
, for
j
= 1,...,
ilo
-1
=
D
j
, for
j
=
ilo
,...,
ihi
=
P
j
, for
j
=
ihi
+1,...,
n
The order in which the interchanges are made is
n
to
ihi
+1, then 1 to
ilo
-1.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.